more grad method

test_grad.py

@@ -7,8 +7,8 @@ import torch
 torch.manual_seed(42)
 
 N = 10
-Niter = 20
-A = torch.rand(N, N, dtype=torch.float64)
+Niter = 30
+A = torch.randn(N, N, dtype=torch.float64)
 T = torch.nn.Parameter(A@A.t()) # a symmetric positive definite transfer matrix 
 
 lnZ = 0.0 
@@ -39,6 +39,20 @@ exact_grad = ((T.grad + T.grad.t())/2) # need to symmetrize since it is an upper
 #or, HF theorem 
 eigenvector_grad= torch.ger(v[:,-1], v[:, -1])/w[-1] # outer product of the leading eigenvector and its transpose
 
+#(5) lnZ using envioment 
+w, v = torch.symeig(T, eigenvectors=True)
+T.grad.zero_()
+
+#try this 
+e = v[:, -1] #environment
+#and this 
+#e = v[:, -1].detach() #environment
+
+loss = torch.log(e@T@e) 
+loss.backward()
+environment_grad = T.grad.clone()
+
 print ((impurity_grad-exact_grad).abs().max().item())
 print ((lnZ_grad-exact_grad).abs().max().item())
 print ((eigenvector_grad-exact_grad).abs().max().item())
+print ((environment_grad-exact_grad).abs().max().item())